Transcript Background on Michaelis-Menten model

Model for Nitrogen Metabolism
for Saccharomyces cerevisiae
based on ter Schure et al. paper
Alondra Vega
Departments of Biology and Mathematics
Loyola Marymount University
February 24, 2011
Outline
• Purpose of Model
• Background on Nitrogen Metabolism
-- Amino acids and enzymes used in reaction
-- Genes involved in nitrogen metabolism
• Background on Michaelis-Menten model
-- Substrates vs. Products
• Demonstrate the model
-- What plays a role and what was left out and why
• Describe differential equations
-- State variables vs. Parameters
• Show model runs and what they mean
• Did the model work?
• Conclusion
--What the model means
--Future Work
Outline
• Purpose of Model
• Background on Nitrogen Metabolism
-- Amino acids and enzymes used in reaction
-- Genes involved in nitrogen metabolism
• Background on Michaelis-Menten model
-- Substrates vs. Products
• Demonstrate the model
-- What plays a role and what was left out and why
• Describe differential equations
-- State variables vs. Parameters
• Show model runs and what they mean
• Did the model work?
• Conclusion
--What the model means
--Future Work
The purpose of this model is to see how nitrogen
metabolism happens in the yeast cell. There are
three main amino acids that were studied in this
model, which are glutamine, glutamate, and alphaketoglutarate. They each have different enzymes
that correspond to their respected reactions. The
goal is to see how nitrogen behaves in this process.
ter Schure et al. tries to demonstrate that ammonia
concentration is responsible for nitrogen metabolism,
which the model will try to demonstrate.
Outline
• Purpose of Model
• Background on Nitrogen Metabolism
-- Amino acids and enzymes used in reaction
-- Genes involved in nitrogen metabolism
• Background on Michaelis-Menten model
-- Substrates vs. Products
• Demonstrate the model
-- What plays a role and what was left out and why
• Describe differential equations
-- State variables vs. Parameters
• Show model runs and what they mean
• Did the model work?
• Conclusion
--What the model means
--Future Work
Background on Nitrogen Metabolism
van Riel & Sontag (2006) IEEE Proc.-Syst. Biol. 153: 263-274
Background on Nitrogen Metabolism
• Amino
Acids of Interest
1) Glutamine
2) Glutamate
3) alpha-ketoglutarate
• Enzymes involved in reactions:
1) glutamine synthetase (GS)
2) GDA
3) NAD-GDH
4) NADPH-GDH
5) GOGAT
Background on Nitrogen Metabolism
•Genes involved in nitrogen metabolism
1) HIS4: Multifunctional enzyme containing phosphoribosylATP pyrophosphatase.
2) GDH1: Synthesizes glutamate from ammonia and alphaketoglutarate.
3) GLN1: Synthesizes glutamine from glutamate and
ammonia.
4) ILV5: Mitochondrial protein involved in branched-chain
amino acid biosynthesis.
5) GDH2: Degrades glutamate to ammonia and alphaketoglutarate.
6) GAP1: Localization to the plasma membrane is regulated
by nitrogen source.
7) PUT4: Transcription is repressed in ammonia-grown cells.
Outline
• Purpose of Model
• Background on Nitrogen Metabolism
-- Amino acids and enzymes used in reaction
-- Genes involved in nitrogen metabolism
• Background on Michaelis-Menten model
-- Substrates vs. Products
• Demonstrate the model
-- What plays a role and what was left out and why
• Describe differential equations
-- State variables vs. Parameters
• Show model runs and what they mean
• Did the model work?
• Conclusion
--What the model means
--Future Work
Background on Michaelis-Menten model
• Why is the Michaelis-Menten model appropriate to use in this
reaction?
- It is appropriate because it is a model of enzyme
kinematics. This means that it relates the reaction rates and
the concentration of the substrates.
• A substrate is a substance that is acted upon an enzyme.
• A product is anything that is produced.
Michaelis-Menten Equation
Figure 1.
Michaelis-Menten Graph
Outline
• Purpose of Model
• Background on Nitrogen Metabolism
-- Amino acids and enzymes used in reaction
-- Genes involved in nitrogen metabolism
• Background on Michaelis-Menten model
-- Substrates vs. Products
• Demonstrate the model
-- What plays a role and what was left out and why
• Describe differential equations
-- State variables vs. Parameters
• Show model runs and what they mean
• Did the model work?
• Conclusion
--What the model means
--Future Work
Demonstrate the model
van Riel & Sontag (2006) IEEE Proc.-Syst. Biol. 153: 263-274
Outline
• Purpose of Model
• Background on Nitrogen Metabolism
-- Amino acids and enzymes used in reaction
-- Genes involved in nitrogen metabolism
• Background on Michaelis-Menten model
-- Substrates vs. Products
• Demonstrate the model
-- What plays a role and what was left out and why
• Describe differential equations
-- State variables vs. Parameters
• Show model runs and what they mean
• Did the model work?
• Conclusion
--What the model means
--Future Work
System of Differential Equations
State Variables vs. Parameters
• A state variable is a variable who is independent, it does not rely
on other variables.
• A parameter is a variable whose quantity or function cannot itself
be precisely determined by direct methods.
State Variables
Parameters
Glutamine
V1 = k1(GDA)0
Glutamate
V2 = k2(GS)0
Alpha-ketoglutarate
V3 = k3(NAD-GDH)0
Nitrogen
V4 = k4(NADPH-GDH)0
V5 = k5(GOGAT)0
D = dilution rate (0.15 h-1)
u = inflow of ammonium and
glucose (10 mol/L)
Note: the k variables are also considered parameters.
Example
V4
V2
V1
V3
V5
van Riel & Sontag (2006) IEEE Proc.-Syst. Biol. 153: 263-274
Outline
• Purpose of Model
• Background on Nitrogen Metabolism
-- Amino acids and enzymes used in reaction
-- Genes involved in nitrogen metabolism
• Background on Michaelis-Menten model
-- Substrates vs. Products
• Demonstrate the model
-- What plays a role and what was left out and why
• Describe differential equations
-- State variables vs. Parameters
• Show model runs and what they mean
• Did the model work?
• Conclusion
--What the model means
--Future Work
What does the model tell us?
Figure 2. This is what
happens when all parameters
are set to the same value. In
this case 2. Nitrogen is
increasing.
Figure 3. Shows what happens
when V5 is changed from a
value of 2 to 5. Nitrogen is still
increasing, but it dips at a faster
time interval, then when they
were in initial state.
What does the model tell us?
Figure 3. Shows what happens to
the system when V4 changes
from 2 to 5. Nitrogen is
increasing. Why do we have
negative values?
Figure 4. Shows what happens to
the system when V3 is changed
from 2 to 5. Nitrogen takes a dip,
but it does not reach zero. After
about 4 seconds, it begins to
increase.
What does the model tell us?
Figure 5. Shows the effect that V2
has when it changes from 2 to a
value of 5. We see that nitrogen
still has a dip that gets close to
zero, but then it begins to
increase.
Figure 6. Shows how the
system changes when V1 is
changed from a value of 2 to
5. Nitrogen is still increasing
in the system.
Outline
• Purpose of Model
• Background on Nitrogen Metabolism
-- Amino acids and enzymes used in reaction
-- Genes involved in nitrogen metabolism
• Background on Michaelis-Menten model
-- Substrates vs. Products
• Demonstrate the model
-- What plays a role and what was left out and why
• Describe differential equations
-- State variables vs. Parameters
• Show model runs and what they mean
• Did the model work?
• Conclusion
--What the model means
--Future Work
Did the model work?
Goal for ter Schure et al. was to prove that the
concentration of ammonium is the main factor of
nitrogen metabolism.
• The system of differential equations, showed that
nitrogen was increasing in all scenarios.
• This means that it is possible that the concentration of
ammonium is one of the main factors in this system.
• There were a couple of discrepancies, such as getting
negative values in some of the graphs. This is due to
the way that the differential equations were set up.
(example glutamine)
Outline
• Purpose of Model
• Background on Nitrogen Metabolism
-- Amino acids and enzymes used in reaction
-- Genes involved in nitrogen metabolism
• Background on Michaelis-Menten model
-- Substrates vs. Products
• Demonstrate the model
-- What plays a role and what was left out and why
• Describe differential equations
-- State variables vs. Parameters
• Show model runs and what they mean
• Did the model work?
• Conclusion
--What the model means
--Future Work
Conclusion
• The model is trying to describe the nitrogen metabolism in yeast
cells.
• It does reach the goal of proving that ammonium is increasing,
but we do not know with how much certainty this occurs by.
Future Work:
• Check how “valid” the system of differential equations really is.
• Look into how the model can be improved. An option would be
to model with partial differential equations.
• Look at the role that the genes play in the system, and try to
model along with the amino acids.
Resources
•ter Schure, E.G., Sillje, H.H.W., Verkleij, A.J., Boonstra,
J., and Verrips, C.T. (1995) Journal of Bacteriology 177:
6672-6675.
•ter Schure, E.G., Sillje, H.H.W., Verkleij, A.J., Boonstra,
J., and Verrips C.T. (1995) Microbiology 141: 1101-1108.
•Biology Dictionary http://www.biology-online.org
•Geneome http://www.yeastgenome.org/cgibin/locus.fpl?locus=CIN5